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Task assignment in tree-like hierarchical structures

Author

Listed:
  • Cem Evrendilek

    (Izmir University of Economics)

  • Ismail Hakki Toroslu

    (Middle East Technical University)

  • Seyedsasan Hashemikhabir

    (Middle East Technical University)

Abstract

Many large organizations, such as corporations, are hierarchical by nature. In hierarchical organizations, each entity, except the root, is a sub-part of another entity. In this paper, we study the task assignment problem to the entities of a tree-like hierarchical organization. The inherent tree structure introduces an interesting and challenging constraint to the standard assignment problem. Given a tree rooted at a designated node, a set of tasks, and a real-valued function denoting the weight of assigning a node to a task, the Maximum Weight Tree Matching (MWTM) problem aims at finding a maximum weight matching in such a way that no tasks are left unassigned, and none of the ancestors of an already assigned node is allowed to engage in an assignment. When a task is assigned to an entity in a hierarchical organization, the whole entity including its children becomes responsible from the execution of that particular task. In other words, if an entity has been assigned to a task, neither its descendants nor its ancestors can be assigned to any task. In the paper, we formally introduce MWTM, and prove its NP-hardness. We also propose and experimentally validate an effective heuristic solution based on iterative rounding of a linear programming relaxation for MWTM.

Suggested Citation

  • Cem Evrendilek & Ismail Hakki Toroslu & Seyedsasan Hashemikhabir, 2017. "Task assignment in tree-like hierarchical structures," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 631-655, August.
    • Handle: RePEc:spr:jcomop:v:34:y:2017:i:2:d:10.1007_s10878-016-0097-6
    DOI: 10.1007/s10878-016-0097-6
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    References listed on IDEAS

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    1. Walteros, Jose L. & Vogiatzis, Chrysafis & Pasiliao, Eduardo L. & Pardalos, Panos M., 2014. "Integer programming models for the multidimensional assignment problem with star costs," European Journal of Operational Research, Elsevier, vol. 235(3), pages 553-568.
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